After actually viewing the season, I believe this comes down to the subtext of the lead up to the 'Not Fade Away' battle. While this is a hypothetical question, it's also illogical. Had Cordelia been there, it would not have come to that particular scenario in 'Power Play'.
Every event that related to Angel's knowledge of the Circle Of the Black Thorn, his secret position as a double agent, his choices as the head of Wolfram & Hart which played into their hands for that role was a direct result of Cordelia's death.
She had a large influence on Angel's decision making in a couple of ways; how she was being affected/victimized and where she stood on the matter. When she didn't approve of how he did something, she had no problem verbally smacking him across the face and I think in part for that reason but also because he was closest to her, he trusted and valued her viewpoint more than anyone's.
So the fact that she was able to give him The Circle (via passing the visions on to him) but NOT able to participate in what he did with that knowledge was the butterfly effect.
Cordy would not have condoned his actions in the double agent role such as giving that baby to The Fell, she probably would have ended up stepping in herself when she realized he was doing it but that's voided by the likelihood that he would not have gone undercover with her around knowing it meant he'd have to hurt her (because he knew going into it that he'd have to make his team feel like he'd betrayed them). She was the most important person in his life alongside Connor, he'd never have the strength to do that to her again after his crisis in season 2. Even though it would be fake this time, it would be real to her and when she found out it wouldn't make a difference, she'd never forgiven him a second time, nor for going behind their backs. Remember in 'You're Welcome', her reaction to the teams' memories being wiped in the Connor reality shift? "you let them rape the memories of the people who trust you!"
(Sidenote: I don't doubt she came to understand the necessity of rewriting Connor, but I can see her never condoning wiping the team's memories, her tone had clearly said "unacceptable!").
There is also the possibility that Fred would not have been killed/taken over by Illyria, Cordy might have stopped her from touching the coffin or have had her occupied elsewhere when it had arrived thus causing it to be handled by someone else by the time Fred got to the lab. No guarantees here, but it's possible.
If we look at the hypothetical scenario presented here, we have to consider that the battle in 'Not Fade Away' was a suicide mission, was it not? At this point, no one was dripping with enthusiasm for life. They at least seemed prepared to not survive. Lorne was the exception in a couple of ways but, I digress.
Angel, in particular, might have felt differently with Cordelia by his side and with the Shanshu still a possibility (remember he thought he signed it away). If Fred had been able to avoid Illyria Wesley would have felt differently as well.
The most sensible subtext though is that with Cordelia around they probably wouldn't have even ended up at Wolfram & Hart which would have given us a completely different season 5 altogether.
I'll give this, if there were logic to Cordelia being present in the exact same battle, I envision her having been in Connor's role in Angel's battle with Hamilton, and just as Connor had she'd have shown up on impulse though Angel would have likely tried to tell her to stay away. Oh, would I have loved for her to receive that line, and I've imagined it:
"They'll destroy you!"
"As long as you're ok they can't!"
Sorry had to have a Cangel fangirling moment with that.
(I'm pretty sure otherwise I've been unbiased, I always am...or intend to be).